It will be 50 years in June since John Profumo, the Minister for War in Harold Macmillan’s Conservative government, was forced to resign because politicians and journalists had stopped pretending to believe his flimsy denials of a short affair with Christine Keeler.

A few days later, Christine Keeler’s sometime landlord and friend, Stephen Ward, an osteopath with a rich and fashionable list of patients, was arrested by the Metropolitan Police and charged under the Sexual Offences Act with being her pimp. His subsequent trial was the biggest scandal of all: put in the frame by unscrupulous policemen, subjected to slurs by the prosecutors, his eventual conviction was a politically motivated miscarriage of justice that still has the power to shock.

The National Portrait Gallery in London is staging an exhibition of photographs and pictures of Christine Keeler and the other protagonists of the Profumo Affair. For people who weren’t alive in 1963, it will help to explain why the affair itself, and the subsequent Ward trial, had such a tremendous impact.

One discovery made by the gallery is getting particular attention. There is a pastel sketch of Christine Keeler made by Stephen Ward, who was a talented artist. His sketches of royalty and celebrities used to appear in The Daily Telegraph. On the back of it is another drawing, of a young woman with a beehive haircut of the sort made famous by the pop singer Helen Shapiro.

In a note written in 1975, Christine Keeler explained: “This is me, but I don’t know who the girl on the back is – she is somebody we just picked up at a bus stop.” The great question now is: who is the girl?

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One suggestion is that she was a hitch-hiker whom Christine Keeler and her boyfriend Noel Howard-Jones picked up at a bus stop near Slough on a hot weekend in July 1961. They were on their way to stay with Stephen Ward at his cottage on the banks of the Thames at Cliveden.

This was the weekend when Stephen Ward took his house party – Christine, the hitch-hiker and others – for an after-dinner swim in Lord Astor’s swimming-pool at Cliveden. Soon afterwards, Lord Astor and Jack Profumo sauntered up to the pool to watch the frolicking. Over the years there have been some lurid accounts of what happened next. The reality was probably quite tame; some splashing, some romping, some innocent malarkey – but nothing X-rated.

Jack Profumo got Christine’s telephone number from Stephen Ward, and a few days later they began their short affair. One of the other guests at Cliveden was a naval attaché at the Soviet Russian embassy, Eugene Ivanov, who gave Christine a lift back to London on the Sunday night.

A couple of years later, journalists spiced up the story of Christine and Jack by reporting that she had been going to bed with Ivanov in the same months that she was going to bed with the minister. Without this embellishment, there would have been no security risk for the Labour Party or for tabloid journalists to play up. And nothing more sensational than a bit of no-strings adultery.

Neither Stephen Ward nor the Security Service believed Christine had been Ivanov’s mistress. In my book An English Affair, I show the reasons why the supposed love triangle is very unlikely. And Christopher Hampton, who has written the script of the forthcoming Andrew Lloyd Webber musical about Stephen Ward, is on record as being equally sceptical.

No one remembers the name, or any other details, about the Slough hitch‑hiker. But it is just as possible that Keeler was referring to a hitch-hiker whom Ward spotted at a bus stop in Oxford Street or Bayswater Road – his favourite cruising grounds when he was trying to pick up the slim-hipped girls he fancied, who looked like naughty boys.

But is the unknown girl with the beehive hair the hitch-hiker whom Keeler remembers? Comparing Ward’s pastel sketch with press photographs from the summer of 1963, my guess is that the sketch is of the witness who was called Miss X at Stephen Ward’s trial.

The police hauled her into court and the hectoring QC who led the prosecution tried to make out that Ward had asked Miss X, who was 19, to perform in bed with a man in front of a two-way mirror. However, to the disappointment of the prosecution, her testimony made clear that Ward had been joking. It was, she agreed, just “a bad joke in bad taste”. There was nothing doing.

Miss X was not a prostitute, nor one of Ward’s many girlfriends, but a social acquaintance whom he had met three or four times. The broadcaster Ludovic Kennedy, who attended every day of Ward’s trial, said of Miss X’s testimony that it “should have been obvious to the meanest intelligence… that so farcical a piece of evidence should never have been allowed to reach the Central Criminal Court”.

The Profumo Affair was the first great cataclysm generated by kiss-and-tell chequebook journalism. Until then, if a politician’s marriage hit the rocks, or a minister was caught in the bushes in St James’s Park with a Guardsman, newspapers tut-tutted, but did not go in for blaring, shaming headlines. After 1963, editors were less deferential of authority, journalists more aggressive in unearthing scandals, and no holds were barred.

Politically, the Profumo Affair was very important. The notion that the Conservative Party was run by out-of-touch toffs, some of whom were having much better sex than ordinary voters, was exploited by the Labour Party and the Daily Mirror so brilliantly that Harold Wilson’s Labour won the 1964 general election by just five seats. If Wilson had lost in 1964, as he would have done without the Profumo Affair to help him fuel a campaign based on the politics of envy, it would have been the fourth election defeat in a row for the old-style Labour Party of trade union hacks, Northern power-brokers, crafty time-servers and Communist sympathisers.

A Labour defeat in 1964 would have brought a new Labour leader – perhaps Anthony Crosland or Roy Jenkins – and almost certainly a version of New Labour 30 years before Tony Blair. The dreary Seventies, with their trade union bully-boys and constant strikes and shortages, would have been very different. So the Profumo Affair has a lot to answer for.

And what of Miss X? Ludovic Kennedy described her as “a tall girl with very black hair and Anglo-Indian features”, which is a reasonable description of the unknown girl in Ward’s sketch. “She was quite pretty in a rather puddingy sort of way”, Kennedy continued, but had a “colourless” personality.

Whereas Christine Keeler and her friend Mandy Rice-Davies gesticulated expressively when they were testifying in court, Miss X kept her arms at her sides like a soldier standing to attention. While the barristers posed their questions, she took deep breaths to help her keep calm.

If the unknown woman in the pastel sketch is indeed Miss X, she is now aged 69 or 70, and has lived in blameless obscurity for half a century. The Metropolitan Police behaved very badly when gathering evidence against Ward, as the police often do in high-profile cases in which politicians and newspapers are clamouring for quick results. They intimidated witnesses, twisted evidence and made the simplest jokes seem dirty or sinister. Miss X was part of the collateral damage.

In “Annus Mirabilis”, the poem that identifies 1963 as the year in which sexual intercourse began, “Between the end of the Chatterley ban / And the Beatles’ first LP”, Philip Larkin wrote that “every life became / A brilliant breaking of the bank, / A quite unlosable game”. But it was not a winning game for Jack Profumo, whose political career was ruined; nor for Stephen Ward, who committed suicide at the end of a trial at which so much false evidence was brought against him; nor for Christine Keeler, who was subsequently jailed for perjury in a related case in which she had been coerced into testifying by the police.

And it was certainly not a brilliant moment for poor, mysterious Miss X, who found herself in the Central Criminal Court, with the eyes of the world on her, standing stiff as a poker, gulping for air, utterly miserable, just because Stephen Ward had once teased her about a two-way mirror.